Essays on economic growth

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FUNDAÇÃO GETULIO VARGAS ESCOLA DE ECONOMIA DE SÃO PAULO

RAFAEL DA SILVA VASCONCELOS

ESSAYS ON ECONOMIC GROWTH

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FUNDAÇÃO GETULIO VARGAS ESCOLA DE ECONOMIA DE SÃO PAULO

ESSAYS ON ECONOMIC GROWTH

Tese apresentada à Escola de Economia de São Paulo da Fundação Getulio Vargas como requisito para a obtenção do título de doutor em economia.

Orientador: Vladimir Kühl Teles

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Vasconcelos, Rafael da Silva.

Essays on Economic Growth / Rafael da Silva Vasconcelos. - 2014. 111 f.

Orientador: Vladimir Kühl Teles

Tese (doutorado) - Escola de Economia de São Paulo.

1. Desenvolvimento econômico. 2. Brasil - Indústrias. 3. Mudança estrutural. I. Teles, Vladimir Kühl. II. Tese (doutorado) - Escola de Economia de São Paulo. III. Título.

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ESSAYS ON ECONOMIC GROWTH

Tese apresentada à Escola de Economia de São Paulo da Fundação Getulio Vargas como requisito para a obtenção do título de doutor em economia.

Área de conhecimento: Macroeconomia Data da aprovação: 17/12/2014

Banca Examinadora:

Prof. Dr. Vladimir Kühl Teles (Escola de Economia de São Paulo)

Prof. Dr. Bernardo Vasconcellos Guimarães (Escola de Economia de São Paulo)

Prof. Dr. Enlinson Henrique Carvalho de Mattos (Escola de Economia de São Paulo)

Prof. Dr. Mauro Rodrigues Jr. (Universidade de São Paulo)

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ACKNOWLEDGMENTS

Although this dissertation appears to have been completed by one person, I hereby acknowledge the help and suggestions of various people.

I am grateful to my advisor Vladimir Teles for all his guidance. I would like to thank the professors of the graduate program from Sao Paulo School of Economics for their instruction. I would also like to thank the members of the thesis committee for all their contributions.

I thank Bernardo Guimarães, Tiago Cavalcanti, and seminar participation at the 42th Meeting of Brazilian Association of Graduate Programs in Economics, the 28th International Business Research Conference, and the Thesis Seminars of Sao Paulo School of Economics for helpful comments and suggestions. I also thank the IBGE for providing us access to confidential firm-level data.

I would like to thank my graduate colleagues and friends. Thanks to Turma do Copão,

players ofItavegas, and college friends for the good times. I also thank Jacqueline Vital, Paulo

Henrique Vaz, and Sammara Cavalcanti each for their individual help. I am very grateful to Stefânia Grezzana for the research partnership and unconditional friendship. I would like to thank my family, my brother - Filipe Vasconcelos - and my stepfather -Amauri Rocha. A special thanks to my mother -Eleir Vasconcelos - for the support and incentives.

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ABSTRACT

This dissertation is a conjunction of three essays on the economic growth field. The first essay investigates the existence of resource misallocation in the Brazilian manufacturing sector and measures possible distortions in it. The second essay demonstrate that there is a distinct pattern of structural change between economies and this pattern differs because there are some factors that distort the relative prices and also affect the output productivity. Finally, using a cross-industry cross-country approach, the third essay investigates the existence of an optimal level of competition to enhance economic growth.

Keywords: Economic development; Brazil - Industries; Structural change. JEL Classification: L16, L60, O47.

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RESUMO

Essa tese é composta por três ensaios sobre crescimento econômico. O primeiro ensaio investiga a existência de resource misallocation no setor manufatureiro brasileiro e mensura

as possíveis distorções ocasionadas. O segundo ensaio demonstra que existe um padrão de mudança estrutural distinto entre países e esse padrão difere porque existem fatores que distorcem os preços relativos e que também afetam a produtividade do produto. Por último, usando uma abordagemcross-industry cross-country, o terceiro ensaio investiga a existência

de um nível ótimo de competição que eleve o crescimento econômico.

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List of Figures

2.1 TFP and price levels in Brazil 18

2.2 Distribution of TFP 20

2.3 Dispersion of input wedges 20

2.4 Allocation efficiency 21

2.5 Alternative reallocation measures 21

2.6 Resource misallocation and Solow residual 21

2.7 Scala wedges 22

2.8 Industry TFP and within-industry efficiency 23

2.9 Taxation exercise 24

3.1 Facts of industry I 44

3.2 Facts of industry II 45

3.3 Numerical exercise 46

3.4 Facts of industry III 47

3.5 Numerical exercise II 47

4.1 Distribution of index competition 69

4.2 Distribution of index competition by countries 69

4.3 Output growth x competition 70

4.4 Output growth x competition II 70

4.5 Simulation 75

B.1Facts of industry IV 93

B.2Facts of industry V 93

B.3Facts of industry VI 94

C.1Output growth x competition III 100

C.2Output growth x competition IV 100

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List of Tables

2.1 Brazil’s manufacturing summary I 18

2.2 Brazil’s manufacturing summary II 19

2.3 Robustness of results 22

2.4 Linkage and complementarity effect 23

3.1 Brazil’s manufacturing sectors 45

3.2 Parameters 46

4.1 Basic results 71

4.2 Basic results for countries 72

4.3 Basic results for countries II 73

4.4 Robustness of results 74

4.5 Robustness of results II 74

4.6 Simulation II 75

A.1Linkage in the Brazilian manufacturing sector 84

C.1Basic results II 97

C.2Basic results for countries III 98

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CHAPTER 1

Introduction

A fundamental question in development economics is why some economies are rich and others poor. To illustrate the income per capita gap across economies consider that the average gross domestic product (GDP) per capita of the richest 10 percent of economies in the year 2010 was a factor of 40-fold that of the poorest 10 percent of economies. In other words, the average person in a rich economy produces in just over 9 days what the average person in a poor economy produces in an entire year. What are the factors that can explain this difference in standard of living across the world today? With this in view, this dissertation is a conjunction of three essays on the economic growth field which we seek a possible responses to this question. One key question is then: What are the sources of low total factor productivity (TFP) in poor economies? The literature has emphasized the possibility that resources may not be efficiently distributed across production opportunities thereby generating lower TFP. This perspective has appeal in understanding productivity differences across economies for at least two reasons. First, in rich economies, it is well established that the reallocation of factors across productive units explains a large portion of productivity growth over time. Second, it is widely recognized that a number of policies and institutions prevalent in poor economies can distort the allocation of factors across productive units. This is what the literature broadly refers to as misallocation. We investigate the existence of resource misallocation in the Brazilian manufacturing sector as well as measuring possible distortions in the chapter 2. Secondarily, to inquire how this misallocation may relate to the economic crisis. For this we use firm-level data for the 1996-2011 period and a similar method of computation as the one developed by Hsieh and Klenow (2009). The results show that there is some variability in the dispersion of inputs for the same level of production between firms and sectors. This finding suggests that there is a misallocation in the Brazilian manufacturing sector. This misallocation decreased between 1996 and 2005 but has been growing since then. We also find that the economic crisis did not have a substantial effect on the aggregate TFP or on the sector’s misallocation. However, small firms in particular seem to be strongly affected in a global crisis. Furthermore, the effects described would be attenuated if we consider linkages and complementarity effects among sectors. Despite Brazil’s well-known high tax burden, there is not evidence that this is the main source of resource misallocation.

Other relevant reason is that the composition of production and employment are an important part of the process of economic development and because similar changes are present even beneath the facade of balanced modern growth. Then, there is a need to check the pattern of the structural change occurring in developing economies, and it will be important to understand output gap between economies. Moreover, there is a pattern of production in the Brazilian manufacturing sector that differs from that observed in the industrialized economies. This pattern is not fully explained by models that focus on the allocation of resources.

From describe above, the aim of chapter 3 is to present a theoretical framework that also explains this pattern observed in developing economies. We will present a multi-sector model of economic growth with structural change. First, we introduce a public good in the production function of the intermediate goods firms, and a government can levy taxes on these firms to finance this public good. We seek to demonstrate that the government would change the allocation of inputs to affect the relative prices of the intermediate goods, mainly because the

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public good would be insufficiently provided or the tax would be excessive. Second, we will be introducing a majority decision to choose the tax system. This environment can accelerate the structure change of production or imply the persistence of harmful structures to economic growth. Third, we also demonstrate that structural change differs between economies basically because there is a resource misallocation. The results of the calibration exercises indicate that the mechanism proposed in this chapter can generate changes in the sectoral composition and they are broadly comparable to the changes we observe in the manufacturing sector in developing economies.

We also shall consider one aspects on which growth theory delivers distinctive predictions in chapter 4. The relationship between economic growth and industrial organization. A faster innovation growth is generally associated with higher turnover rates. Moreover, competition appears to be positively correlated with output growth. In contrast, the schumpeterian growth paradigm can partially rationalize the negative correlation between competition and output growth. In addition, it can account for several interesting facts about competition and growth which no other growth theory can explain. Given a well-know fact that the greater technological level, the greater economic growth. Thus, competition and growth display an inverted-U relationship: starting for an initially low level of competition, higher competition

stimulates innovation and output growth; starting from a high initial level of competition, higher competition has a negative effect on innovation and output growth.

Then, the chapter 4 aims to clarify how the degree of competition and the output growth rate are correlated. This correlation would be distinct and dependent on the distance that the industry-country is to the technological frontier and the idiosyncrasies of each industry-country. We show the effect of varying the competition level on the growth of product for the industries in the developing economies. Thus, the difference in competition industry-country level would be a channel to explain the output per worker gap between economies. Our results imply that there is an inverted-U relationship between competition and the growth rate of output across

industries and countries. The same is also distinctive among industrialized and developing economies. This effect on the growth rate depends on the competition measurement used.

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CHAPTER 2

Misallocation in the Brazilian manufacturing sector

Abstract

This chapter investigates the existence of resource misallocation in the Brazilian manufacturing sector and measures possible distortions in it. Using a similar method of measurement to the one developed by Hsieh and Klenow (2009) and firm-level data for 1996-2011 we find evidence of misallocation in the manufacturing sector during the observed period. Moreover, our results show that misallocation has been growing since 2005, and it presents a non-smooth dynamic. Significantly, we find that the Brazilian manufacturing sector operates at about 50% of its efficient product. With this, if capital and labor were optimally reallocated between firms and sectors we would obtain an aggregate output growth of approximately 110-180% depending on the mode in which the capital share is measured. We also find that the economic crisis did not have a substantial effect on the total productivity factor or on the sector’s misallocation. However, small firms in particular seem to be strongly affected in a global crisis. Furthermore, the effects described would be attenuated if we consider linkages and complementarity effects among sectors. Finally, despite Brazil’s well-known high tax burden, there is not evidence that this is the main source of resource misallocation. Keywords: Resource misallocation, TFP, Firm-level data.

1. Introduction

There are significant differences in output per worker between industrialized and developing countries. With this in aim, the literature of economic growth argument that this gap is primordially due to the differences of technical progress and the savings rate between countries (Lucas, 1988). However, the allocation of inputs across sectors and countries is also distinct. Most of the total factor productivity (TFP) could be distinct and unmeasured between sectors and countries. According to Hopenhayn (1992), the heterogeneity of productive structures and different economic conditions could result in the suboptimal allocation of inputs. From that, some of the economic literature investigates the misallocation of resources and its impact on economic development. With this in view, this chapter will focus on the relationship between the resource misallocation at firm-level, the aggregate TFP, and the economic growth.

In this context, Hsieh and Klenow (2009) examine the misallocation of firms’ inputs. The authors use the change in value of the marginal product of inputs across firms as a measurement to show how the misallocation of resources at the firm-level affects aggregate TFP. Their results imply that if the manufacturing sectors of India and China had the same degree of misallocation as the U.S. manufacturing sector, their aggregate products would grow approximately 30-50% and 40-60%, respectively. From an empirical and theoretical point of view, this work exposes the importance of relative prices, the factors that distort these prices, and how all this influences misallocation (Restuccia and Rogerson, 2013). Moreover, many other studies explain how differences in the aggregate TFP between countries are affected by resource allocation (Foster et al., 2008; Collard-Wexler et al., 2011) and how economic policies affect this allocation (Restuccia and Rogerson, 2008; Bartelsman et al., 2013; Buera and Shin, 2013).

The fundamental thesis of this chapter is that the allocation of inputs between firms affects the aggregate TFP. Consequently, relative prices are fundamental to this relation. Prices are

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subject to political, social and economic conditions, which can affect the decision making process and influence the allocation of inputs (Melitz, 2003; Melitz and Ottaviano, 2008; Restuccia and Duarte, 2012). Examples of allocative restrictions are a flawed tax system1 _or

a labor market with low flexibility2_{; these restrictions impact relative prices, the allocation of}

a firm’s inputs and the aggregate TFP. Attacking these restrictions, Restuccia and Rogerson (2008) find that much of the observed decrease in the TFP in some countries originates from the fact that tax rates are negatively correlated with the optimal allocation of inputs. Moreover, Restuccia and Rogerson (2013) suggest that any change in the tax rates that does not consider firm characteristics would lead to a further loss in the aggregate TFP.

Misallocation of resources could also be correlated with economic changes. How would misallocation of resources affect and be affected in periods of economic crisis? During economic crisis, social planners will make decisions envisioning the attenuation of the crisis’ effects, such as expansionary fiscal policies that are used to encourage economic growth during recessions. However, depending on the crisis and the policy adopted, a growth in the misallocation of resources can occur, because relative prices can be distorted in this situation (Oberfield, 2013). For example, an asymmetrical increase in taxes or subsidies among sectors changes the relative prices and affects the product and income structure. This change would be permanent or temporary and would involve gains or losses in the aggregate economy.

Therefore, this chapter investigates the existence of misallocation of resources in the Brazilian manufacturing sector and measures possible distortions. This chapter also inquires how this misallocation may relate to economic crisis. We use firm-level data for 1996-2011 and a similar method of computation as the one developed by Hsieh and Klenow (2009). Brazil’s economy is the focal point because of its various peculiarities. A high tax burden, a weak judicial system and a poor infrastructure in Brazil could result in a high misallocation of resources. Figure 2.1 presents Brazil’s price and TFP levels. According to this figure, the price of capital is low compared with the U.S. economy. Moreover, comparing with the global economic crisis, these prices differ from the average prices in the Brazilian economy. Thus, capital loses its relative value and this fact implies that the value of the average product falls to the same level of capital. This result could be a sign of misallocation.

The results show that there is some variability in the dispersion of inputs for the same level of production between firms and sectors. This finding suggests that there is a misallocation of resources in the Brazilian manufacturing sector. This misallocation decreased between 1996 and 2005 but has been growing since then. We measure how much aggregate manufacturing output in Brazil could increase if capital and labor were reallocated to equalize marginal products across firms within 4-digit sector to the extent observed in the U.S. This method is similar to the one developed by Hsieh and Klenow (2009). We find that moving toU.S. efficiencywould

increase aggregate growth by 160-180%. We also use production factors parameterized using Brazilian firm-level data. In this case, we find that moving toBrazilian Firm-Specific efficiency

would increase aggregate growth by 110-130%.

Regarding economic crisis, the focus here is restricted to the Asian financial crisis (1998), the Domestic crisis (2002) and the Subprimes crisis (2008). The Asian and Subprimes crisis could reduce the availability of capital in the Brazilian economy. The Brazilian crisis in 2002 was caused by political uncertainties. The results showed that in periods of crisis, the change of misallocation was more severe for small firms in the Brazilian market.

Thus, this chapter contributes to the literature by documenting misallocation of resources in the Brazilian manufacturing sector and suggests explanations for this misallocation. The relevance of this chapter is confirmed by the magnitude of the results and can help to understand the persistence of the differences in output per capita between countries. The results suggests

1_{See Romer and Romer (2010) and Kneller et al. (1999) for example.}

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that this difference is potentiated by misallocation of resources. In the Brazilian manufacturing sector, this potentiality is substantial.

The remainder of this chapter is organized as follows. Section 2 describes the basic framework for the measurement of misallocation of resources. Section 3 presents the data and the empirical results. Section 4 contains further discussion regarding the measurement of misallocation. Finally, section 5 concludes.

2. Basic framework

We characterize a simple framework similar to the framework constructed by Hsieh and Klenow (2009) and utilized by others authors. Therefore, we will use the monopolistic competition model with heterogeneous firms. Misallocation of resources at the firm-level affects the aggregate TFP in this model. Thus, we quantify how much of the change in the Solow residual results from changes in input allocation.

2.1. Environment. Suppose a closed economy without government in an infinite life-time 𝑡 ∈ [0,∞). We assume there is a single final good𝑌𝑡 produced by a representative firm in a perfectly competitive final output market. This final good combines the intermediate good𝑌𝑠𝑡 of𝑆manufacturing sectors using Cobb-Douglas technology

(2.1) 𝑌𝑡=∏︁

𝑠∈𝑆 𝑋𝜃𝑠

𝑠𝑡,

where𝜃𝑠 ∈(0,1)and∑︀

𝑠∈𝑆𝜃𝑠 = 1. The profit maximization by the final good producer implies that𝜃𝑠 =𝑃𝑠𝑡𝑋𝑠𝑡/𝑃𝑡𝑌𝑡for each sector. Thus,𝜃𝑠represents the weight of a sector in the economy. Therefore,𝑃𝑠𝑡 is the price of the intermediate good for each sector and 𝑃𝑡 = ∏︀

𝑠∈𝑆(𝑃𝑠𝑡/𝜃𝑠)𝜃𝑠 represents the price of the final good. The price of the final good is a numeraire.

Each sector combines heterogeneous goods𝑋𝑖𝑠𝑡for𝐼𝑠 firms using CES technology

(2.2) 𝑋𝑠𝑡 =

(︃ ∑︁

𝑖∈𝐼𝑠

𝑋

𝜎−1

𝜎

𝑖𝑠𝑡 )︃_𝜎𝜎₋₁

,

where𝜎∈(0,∞). Assume that the firm’s production function is

(2.3) 𝑋𝑖𝑠𝑡=𝑀𝑖𝑠𝑡𝐾𝛼𝑠

𝑖𝑠𝑡𝐿1𝑖𝑠𝑡−𝛼𝑠,

where𝛼𝑠∈(0,1)is capital share,𝑀𝑖𝑠𝑡is TFP,𝐿𝑖𝑠𝑡is a labor factor, and𝐾𝑖𝑠𝑡is physical capital. Assume that the capital share is sector-invariant. Assume price-taking consumers so that all the final goods are produced and subsequently consumed by consumers.

There are two relevant points regarding the firm’s production function. First, we require that𝛼 does not change within sectors. It is plausible that the input proportion does not vary substantially between firms in the same sector. However, this variability can exist and this fact potentiates the misallocation of resources3_{. Therefore, we will relax this assumption in}

the next subsection. Second, the functional form of the production function could imply that misallocation of resources is nothing other than the technological heterogeneity of firms. We are aware of this problem and we will check the key parameters in the quantitative analysis section, mainly𝛼and𝜎.

3_{For example, employees are more productive in some firms compared with other firms because some unmeasured}

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2.2. The measurement of distortions on inputs. We will identify the distortions on inputs that will affect their market values. According to Hsieh and Klenow (2009), because there are two separable factors of production, we can identify distortions. We denote distortions that increase the marginal products of capital and labor by the same proportion as an output distortion𝜏𝑌 𝑖𝑠. In turn, we denote distortions that raise the marginal product of capital relative to labor as the capital distortion𝜏𝐾𝑖𝑠. These distortions vary across firms, sectors, and time. For example,𝜏𝑌 𝑖𝑠is high because of a legal restriction on prices or high transport costs and𝜏𝐾𝑖𝑠can represent the credit limit. In this context, the firm’s profit is

(1−𝜏𝑌 𝑖𝑠)𝑃𝑖𝑠𝑡𝑋𝑖𝑠𝑡−𝑤𝑖𝑠𝑡𝐿𝑖𝑠𝑡−(1 +𝜏𝐾𝑖𝑠)𝑅𝑡𝐾𝑖𝑠𝑡,

where 𝑤𝑖𝑠𝑡 is the wage and 𝑅𝑡 is the cost of capital. These the costs are time-variant. The maximization problem of each firm implies that

(2.4) 𝑃𝑖𝑠𝑡 =

𝜎 𝜎−1

(︂ 𝑅𝑡 𝛼𝑠

)︂𝛼𝑠(︂ 𝑤𝑖𝑠𝑡

1−𝛼𝑠 )︂1−𝛼𝑠

(1 +𝜏𝐾𝑖𝑠)𝛼𝑠

𝑀𝑖𝑠𝑡(1−𝜏𝑌 𝑖𝑠).

Thus, the distortions affect the good price of each firm. Moreover, this effect is potentiated by capital share.

Suppose allocative choice depends only on technological level. However, inputs can have their values distorted (Hsieh and Klenow, 2009). Thus, resource allocation would result from differences between the input marginal revenue among firms. The marginal revenue product of labor is proportional to revenue per worker. The marginal revenue product of capital is proportional to the revenue-capital ratio. These facts are given, respectively, by

𝑀 𝑅𝑃 𝐿𝑖𝑠𝑡 =

1

1−𝜏𝑌 𝑖𝑠𝑤𝑖𝑠𝑡, (2.5a)

𝑀 𝑅𝑃 𝐾𝑖𝑠𝑡 =

1 +𝜏𝑌 𝑖𝑠

1−𝜏𝑌 𝑖𝑠𝑅𝑡. (2.5b)

Intuitively, ex post the marginal revenue of inputs is equalized. However, ex ante the marginal revenue of inputs is relatively small for some firms. This factor would reduce incentives for firm efficiency.

We then derive aggregate TFP as a function of misallocation of resources at the firm-level. Solving the allocative equilibrium between sectors we have 𝐿𝑠𝑡 = ∑︀

𝑖∈𝐼𝑠𝐿𝑖𝑠𝑡 and 𝐾𝑠𝑡 =

∑︀

𝑖∈𝐼𝑠𝐾𝑖𝑠𝑡, the total input in each sector. Therefore, in equilibrium, these variables can be

rewritten as a function of the value of the marginal product of inputs in each sector4_{. We define}

𝐿𝑡=∑︀

𝑠∈𝑆𝐿𝑠𝑡and𝐾𝑡 = ∑︀

𝑠∈𝑆𝐾𝑠𝑡as aggregate labor and aggregate capital, respectively. The real and nominal TFP at the firm-level are, respectively,

𝑇 𝐹 𝑃 𝑅𝑖𝑠𝑡 ≡𝑀𝑖𝑠𝑡=

𝑋𝑖𝑠𝑡 𝐾𝛼𝑠

𝑖𝑠𝑡𝐿1𝑖𝑠𝑡−𝛼𝑠 ,

𝑇 𝐹 𝑃 𝑄𝑖𝑠𝑡 ≡𝑃𝑖𝑠𝑡𝑀𝑖𝑠𝑡= 𝑃𝑖𝑠𝑡𝑋𝑖𝑠𝑡

𝐾𝛼𝑠

𝑖𝑠𝑡𝐿1𝑖𝑠𝑡−𝛼𝑠 .

Using equations 2.5a and 2.5b we get5

𝑇 𝐹 𝑃 𝑅𝑖𝑠𝑡 ∝(𝑀 𝑅𝑃 𝐾𝑖𝑠𝑡)𝛼𝑠₍_{𝑀 𝑅𝑃 𝐿𝑖𝑠𝑡}₎1−𝛼𝑠 _∝ (1 +𝜏𝐾𝑖𝑠)

𝛼𝑠 1−𝜏𝑌 𝑖𝑠 .

4_{See the appendix A for details.} 5_{More specifically,}_{𝑇 𝐹 𝑃 𝑅}

ist= (︁

σ σ−1

)︁ (︁ R𝑡

α𝑠

)︁α𝑠(︁ w𝑖𝑠𝑡 1−α𝑠

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A high 𝑇 𝐹 𝑃 𝑅 may result in input distortion. Therefore, we can obtain the TFP at the sector-level by

(2.6) 𝑇 𝐹 𝑃𝑠𝑡 =

[︃ ∑︁

𝑖∈𝐼𝑠

(︂

𝑀𝑖𝑠𝑡𝑇 𝐹 𝑃 𝑅𝑠𝑡 𝑇 𝐹 𝑃 𝑅𝑖𝑠𝑡

)︂𝜎−1]︃ 1

𝜎−1 ,

where𝑇 𝐹 𝑃 𝑅𝑠𝑡is a geometric average between the revenue of inputs in each sector6. Thus, 𝑇 𝐹 𝑃𝑡 =∏︁

𝑠∈𝑆

𝑇 𝐹 𝑃𝜃𝑠

𝑠𝑡.

Misallocation of resources at the firm-level affects aggregate TFP. This effect depends on the weight of each sector in the final good𝜃𝑠 and the degree of substitution of intermediate goods 𝜎. Moreover, the misallocation effect will depend on the capital share of each sector,𝛼𝑠.

Equation 2.6 is the key of the quantitative analysis. In addition, assume that {log𝑀𝑖𝑠𝑡,log(1−𝜏𝑌 𝑖𝑠),log(1 + 𝜏𝐾𝑖𝑠)}has a multivariate lognormal distribution. We define a standard deviation onlog(1−𝜏𝑌 𝑖𝑠)and log(1 +𝜏𝐾𝑖𝑠) as𝜑𝑌 and 𝜑𝐾, respectively, and also define covariance between these variables as𝜑𝑌 𝐾. Thus7,

(2.7) log𝑇 𝐹 𝑃𝑠𝑡 = 1

1−𝜎log𝐸𝑡{𝑇 𝐹 𝑃 𝑄 𝜎−1

𝑖𝑠𝑡 } − 𝜎

2𝜑 2

𝑌 − (︂

𝛼𝑠+𝛼2

𝑠(𝜎−1)

2

)︂

𝜑2_𝐾+𝜎𝛼𝑠𝜑𝑌 𝐾.

Therefore, 𝑇 𝐹 𝑃 by sector is equal to the weighted average of 𝑇 𝐹 𝑃 𝑄 at firms in the sector less the variance of𝑇 𝐹 𝑃 𝑅. This variance consists of distortion factors on resource allocation. Thus, distortions on aggregate TFP can be summarized by the variance of𝑇 𝐹 𝑃. Furthermore, the misallocation extent is worse depending how much dispersed is the marginal product8_.

Moreover, this effect is potentiated by the correlation between distortions in product. In this case, if we have a high distortion in product and a small distortion in capital, a large part of the product distortion derives from the labor factor.

This structure implies

𝑋𝑖𝑠𝑡∝

(1−𝜏𝑌 𝑠𝑖)

(1 +𝜏𝐾𝑠𝑖)𝛼𝑠𝑀𝑖𝑠𝑡

and thus the distortion of resource allocation affects the efficiency of each firm. How

𝑌𝑡= ∏︁

𝑠∈𝑆 (︃

∑︁

𝑖∈𝐼𝑠

𝑋𝜎−𝜎1

𝑖𝑠𝑡 )︃_𝜎𝜎𝜃𝑠₋₁

also affects the final good. The magnitude of this effect will depend on the degree of substitution between sectors and the importance of each sector to the economy. The worse the resource allocation is at the firm-level, the worse the aggregate allocation. This result implies inefficient production at both the firm-level and the aggregate level. Moreover, the allocations distinct among firms imply that productivity has a dispersed distribution. In this case, a high extension of misallocation of resources implies a greater loss of aggregate efficiency.

6_More _{specifically,} _{𝑇 𝐹 𝑃 𝑅}

st =

(︁ σ σ−1

)︁ (︁

M RP K𝑠𝑡

α𝑠

)︁α𝑠(︁ M RP L𝑠𝑡

1−α𝑠

)︁1−α𝑠

, where

𝑀 𝑅𝑃 𝐿st,∑︀i∈I𝑠

𝑤ist

(1−𝜏Y is)P_P𝑖𝑠𝑡_𝑠𝑡X_X𝑖𝑠𝑡_𝑠𝑡

and𝑀 𝑅𝑃 𝐾st,∑︀i∈I𝑠

𝑅t

1−τ𝑌 𝑖𝑠 1+τ𝐾𝑖𝑠

P𝑖𝑠𝑡X𝑖𝑠𝑡

P𝑠𝑡X𝑠𝑡 .

7_{See the appendix A for details.}

8_{The use of the multivariate log normal distribution implies that}_{𝑇 𝐹 𝑃} _{also varies with the number of firms in}

each sector. Thus,𝐼sis time-variant and we could have a drop in𝑇 𝐹 𝑃 simply because a firms’s concentration in

some sector increased. According Restuccia and Rogerson (2013) there is no apparent loss or change of intuition in terms of theoretical framework. However, in the quantitative analysis we appropriately control this variable by varying the sector concentration to avoid this effect.

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2.3. Optimal allocation. The degree of misallocation is more relevant than the misallocation extension, or how far the current product is from the product implied by optimal allocation. Similarly to Hsieh and Klenow (2009), we can obtain the optimal allocation of inputs that maximizes the sector’s product subject to the availability of inputs. In each time period, then optimal final good is

(2.8) 𝑌_𝑡𝐸 =∏︁

𝑠∈𝑆 ⎡

⎣ ∑︁

𝑖∈𝐼𝑠

(︃

𝑀𝑖𝑡(︁𝛼𝑠 𝛼𝐸𝐾𝑠𝑡

)︁𝛼𝑠(︂1−𝛼𝑠 1−𝛼𝐸𝐿𝑠𝑡

)︂1−𝛼𝑠)︃𝜎−1

⎤

⎦

𝜃𝑠 𝜎−1

,

where𝛼𝐸 ₌_𝜕_ln_𝑌𝐸

𝑡 /𝜕ln𝐾𝑠𝑡and1−𝛼𝐸 =𝜕ln𝑌𝑡𝐸/𝜕ln𝐿𝑠𝑡such that𝑌𝑡𝐸 is the optimal final good implied by efficient allocation in sectors of the economy9_.

We assume now that 𝛼 can change among all firms, for example, a firm with specific technology that becomes more efficient. Therefore, Oberfield (2013) suggests that misallocation could occur in each sector. Otherwise, there exists unmeasurable technological heterogeneity at the firm-level, and this would imply an inefficiency on the aggregate product. Thus, the allocation of inputs that maximizes the product at the sector-level would not necessarily be the same allocation of inputs that maximizes the aggregate product. Given the availability of inputs in the economy, we can obtain the optimal allocation of these factors to maximize the final good. In this situation, the optimal final good is

(2.9) 𝑌_𝑡𝑀 =∏︁

𝑠∈𝑆 ⎡

⎣ ∑︁

𝑖∈𝐼𝑠

(︃

𝑀𝑖𝑠𝑡(︁ 𝛼𝑖 𝛼𝑀𝜃𝑠𝐾𝑡

)︁𝛼𝑖(︂ 1−𝛼𝑖 1−𝛼𝑀𝜃𝑠𝐿𝑡

)︂1−𝛼𝑖)︃𝜎−1

⎤

⎦

𝜃𝑠 𝜎−1

,

where𝛼𝑀 =𝜕ln𝑌𝑡𝑀/𝜕ln𝐾𝑡and1−𝛼𝑀 =𝜕ln𝑌𝑡𝑀/𝜕ln𝐿𝑡such that𝑌𝑡𝑀 is the optimal final good given by efficient allocation within sectors10_.

For equations 2.1 and 2.8 we can determine that the degree of misallocation of resources within-sectors is𝑀𝑡 = 𝑌𝑡/𝑌𝐸

𝑡 . For equations 2.8 and 2.9 we can determine that the degree of misallocation of resources between-sectors is𝑀 𝐵𝑡 = 𝑌𝐸

𝑡 /𝑌𝑡𝑀. Furthermore, the total effect of misallocation is given by the relationship between these two measurements,

(2.10) 𝑀 𝑊𝑡*𝑀 𝐵𝑡= 𝑌𝑡

𝑌𝑀 𝑡

.

Thus, we have a measure of the degree of misallocation of resources. For a given aggregate of input in each time period, the maximum output is the efficient output, and the greater the degree of misallocation of resources. However, computing𝛼𝐸 _and_𝛼𝑀 _{is one of the difficulties in this}

9_{More specifically,}

𝛼E₌∑︁ i∈I𝑠

𝛼s [︁

𝑀ist (︀

𝛼s𝐾st/𝛼E )︀α𝑠(︀

(1−𝛼s)𝐿st/(1−𝛼E)

)︀1−α𝑠]︁σ−1

∑︀ j∈I𝑠

[︁

𝑀jst(𝛼s𝐾st/𝛼E)α𝑠((1−𝛼s)𝐿st/(1−𝛼E))

1−α𝑠]︁σ

−1.

In the quantitative analysis section, we will use this equation for compute a within-industry effects on the misallocation of resources.

10_{More specifically,}

𝛼M =∑︁

s∈S

𝜃s ∑︁

i∈I𝑠

𝛼i [︁

𝑀ist(︀𝛼i𝐾t/𝛼M)︀ α𝑖(︀

(1−𝛼i)𝐿t/(1−𝛼M))︀

1−α𝑖]︁σ−1

∑︀ j∈I𝑠

[︁

𝑀jst(𝛼j𝐾t/𝛼M)α𝑗((1−𝛼j)𝐿t/(1−𝛼M))1 −α𝑗]︁σ

−1.

In the quantitative analysis section we use this equation for compute the between-industry effect on the misallocation of resources. Furthermore, if the capital intensity does not change between firms, similar to Hsieh and Klenow (2009), thus𝛼M ₌ ∑︀

s∈S𝜃s𝛼s. In this case, changes in𝛼M would only be due to changes in the

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chapter. Moreover, if the inputs’ availability is time-variant, then the parameters𝛼𝐸 _and_𝛼𝑀 can change over time11_{. In the quantitative analysis section we will detail the strategy to impute}

these parameters.

If the resources are efficiently allocated in each sector, we can obtain that 𝛼𝐸𝑃

𝐸 𝑖𝑠𝑡𝑋𝑖𝑠𝑡𝐸

𝐾𝐸 𝑖𝑠𝑡

=𝛼𝑠𝑃𝑠𝑡𝑋𝑠𝑡 𝐾𝑠𝑡

for each firm and time period. Thus, identical to Oberfield (2013), we define the capital wedge of each firm as parameters of deviation in relation to the efficient case (within-industry)

𝑇 𝐾𝑖𝑠𝑡= 𝑃𝑖𝑠𝑡𝑋𝑖𝑠𝑡/𝐾𝑖𝑠𝑡

𝑃𝐸

𝑖𝑠𝑡𝑋𝑖𝑠𝑡𝐸 /𝐾𝑖𝑠𝑡𝐸 .

Equivalently, the labor wedge is given by

𝑇 𝐿𝑖𝑠𝑡= 𝑃𝑖𝑠𝑡𝑋𝑖𝑠𝑡/𝐿𝑖𝑠𝑡

𝑃𝐸

𝑖𝑠𝑡𝑋𝑖𝑠𝑡𝐸 /𝐿𝐸𝑖𝑠𝑡 .

Furthermore, we define the scala wedge as

(2.11) 𝑇𝑖𝑠𝑡=𝑇 𝐾𝑖𝑠𝑡𝛼𝑖𝑇 𝐿1𝑖𝑠𝑡−𝛼𝑖.

For equation 2.11, the firm’s scala wedge describe the relationship between the output at firm-level and the misallocation of resources. The greater the scala wedge, the greater dispersion of the output among firms and, consequently, the greater the input distortion.

3. Data and quantitative analysis

3.1. Data. In this subsection we present the firm-level data used to measure the misallocation of resources in the Brazilian manufacturing sector. We also briefly present the aggregate manufacturing sector database used.

3.1.1. Brazilian Firm-level data. We use firm-level data from the National Survey of

Industries constructed by the Brazilian Institute of Geography and Statistics between 1996 and 2011. This survey obtains information on the economic situation at the firm-level in the manufacturing sector. This information includes employees, wages and salaries, revenues, costs and expenses, investment, depreciation, output and intermediate consumption. This information constitutes the collection unit of this survey according to the activity categories. The database is an unbalanced panel of 40,000 firms on average for each year and each firm has at least 30 employees. In 1996 this survey had approximately 30,000 firms and grew to 50,000 in 2005.

The greatest difficulty in this chapter is the construction of firm-level capital variables. This database collects information regarding the investment in machinery, vehicles, buildings and land. Then, we use the perpetual inventory method to estimate gross fixed capital stock at the firms. Therefore, we assume that the depreciation rate is 5%, 10% and 20%, respectively, for machinery, land and buildings and vehicles, identical to Oberfield (2013). Initial capital stocks are computed from reported depreciation and investment in the first observation. We impute that the physical capital stock is missing if investments do not exist in any time period of the sample12_{. In addition, the physical capital stock was deflated by the Brazilian general price}

index.

11_{Regarding the quantitative analysis, the fact that the optimal intensity is time-variant makes the measurement}

dynamically complicated. For example, if the total output in some sectors does not change in the time period, but there is growth in the inputs available, then we will have an apparent increase in the inefficiency allocation. However, if total output continue to change in a short time, then the intensity factor changes and there is a distance from inefficient allocation stabilization. Therefore, we calculate how far the current product by the optimal allocation is, and this calculation does not imply problems in the extensive margin.

12_{Investments cannot exist in all time periods for some firms. Thus, it is not possible to verify if this is really}

missing data.

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Labor remuneration is annual wages paid to blue and white collar workers. This remuneration is corrected by the operation days of each firm. Therefore, wages were deflated by the Brazilian national consumer price index. The value added was defined as the industrial gross values of output deduct the industrial operating cost. The value added also was deflated by the Brazilian general price index. Moreover, we reclassified firms using the International Standard Industries Classification (ISIC) code system. The disaggregation occurred at the 4-digit level of ISIC Code Rev 3.1, which does not significantly reduce the sample. We did not use the sectors comprising less than four firms. Since the chapter focuses on manufacturing firm, we eliminate non-manufacturing observations. We also were excluded the extreme outliers in the results. We excluded 1% of firms with the higher product in each sector-time, and we excluded 1% of firms with the lower product.

Table 2.1 presents the characterization of the Brazilian manufacturing sector between 1996 and 2011. In general, we can see that cost of capital is greater than the cost of a worker. Moreover, the workers and wage per worker increased significantly over time. Another relevant and alarming point is the size of the tax13_{. The size of the tax is equivalent to one-third of the}

wage per worker. Table 2.2 shows some characteristics of each sector, on average, between 1996 and 2011. In this table a ratio wage/value added varies widely among sectors. Taxation also changes but on a smaller scale. The manufacture of food products has the largest share of firms, employees, and export products. The tax represented 7.6% of the value added in this sector. However, this was 28.7% of the total tax paid by the manufacturing sector. The manufacture of chemicals and chemical products is the largest importer. Finally, the manufacture of coke and refined petroleum products is more concentrated and has the lowest intensity labor. However, this manufacture have the second most aggregate value in the aggregate manufacturing sector.

3.1.2. Aggregation data. We use the Industrial Statistics Database (INDSTAT) of the

United Nations Industrial Development Organization (UNIDO). This database contains time series data from 1990 forward. Data are available for country, year and ISIC at the 4-digit levels of ISIC (Revision 3), which comprises 151 manufacturing sectors and sub-sectors. This database comprises the number of establishments, number of employees, wages and salaries, output, value added and gross fixed capital formation. The initial capital stock is computed by the average gross fixed capital formation in each sector-country. This database also is reclassified using the 4-digit level of ISIC Code Rev 3.1. With this reclassification, we can compare the manufacturing sectors.

3.2. Quantitative analysis. We will investigate the existence of misallocation of resources in the Brazilian manufacturing sector. Using the theoretical framework presented at equations 2.6 and 2.7 and the data described in the previous subsection. We will also assess the degree of misallocation from equations 2.10 and 2.11. Again, we do not known the production function of each firm. Thus, the observed differences in the intensity of factors reflect the distortions or the technological heterogeneity. Therefore, we will use essentially two specifications.

The first specification assumes that all firms within-sector have the same factor intensities and that any differences in factor expenditures reflect distortions (U.S. Industry Shares). To parameterize these, we assume that factor intensities are the same as those of corresponding U.S. industries and that these U.S. industries are, on average, undistorted. We use expenditure data from the INDSTAT to compute the cost shares for the relevant industries in the U.S. for 200014_{. This specification is similar to that used by Hsieh and Klenow (2009).}

13_{In this database, taxes refers to those effectively paid on employees and production by each firm.}

14_{We also impute these parameters based on other years. However, the dynamics and the results extension do not}

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The second specification proceeds under the assumptions that all long-run differences in factor expenditure shares reflect differences in underlying technology rather than distortions (Brazilian Firm-Specific Shares). The panel structure of the data can be used to infer the production parameters of each firm. In particular, we assume that while a firm may face a distortion in a particular year, it is, on average, undistorted. To this end, we compute the parameters of a single firm’s production function as follows: in each year, we compute the log of the ratio of nominal expenditure on capital to nominal expenditure on labor. Under the assumption that, for each firm, the median of this quantity over all the years that the firm is in the sample reflects an undistorted choice of inputs, the parameters of the production function can be backed out accordingly. This specification is similar to that used by Oberfield (2013).

3.2.1. Basics results. Figure 2.2 presents the distribution of the logarithm of TFP in the

Brazilian manufacturing sector arbitrarily for 1996, 2005, and 2011. Fundamentally, we are interested in the dispersion of TFP. The more disperse TFP, the greater can be the misallocation. A high dispersion implies that some firms are more able to produce output with the same amount of inputs, given the technology process in each sector. According to this figure, the dispersion is relatively elevate in each time period. Furthermore, the median is greater than the average for the time periods. Therefore, the distribution of TFP is asymmetric. These two points suggest that there exists misallocation of resources at the firm-level in the Brazilian manufacturing sector. Furthermore, the firm-level shows that the mass of firms with lower TFP enhances in the time periods. This finding suggests that some variation of the aggregate allocation may occur because of misallocation in the low-tech firms, generally, the small firms.

Considering this, figure 2.3 present the dynamics of input wedges for two arbitrary percentiles of firms. For each year, this figure shows a measure of dispersion of capital and labor wedges, the log deviations between the 90th and 10th percentiles and between the 75th and 25th percentiles of the respective distributions among firms in the sample from 1996–2011. The first dynamic represents a gap between the 10th and 90th percentile of the aggregate product and another between the 25th and 75th. The distribution of inputs in the Brazilian manufacturing sector is excessively unequal and time-variant. The firm’s capital in the 90th percentile of the productivity is 4 (U.S. Industry Share) or 3 (Brazilian Firm-Specific Share) times greater than the capital firms in the 10th percentile. Regarding the firm’s labor these coefficients would be 2 (U.S. Industry Share) or 2.75 (Brazilian Firm-Specific Share). Note that there is not a clear trend of the input wedges, mainly between 1996 and 2001. Similarly, no clear trend occurs between the 25th and 75th percentiles, but these coefficients are smaller.

This result above suggests that there is some variability in the dispersion of inputs. In addition, there exists misallocation of resources in the Brazilian manufacturing sector, and these results also suggest that this misallocation is time-variant. When we use the U.S. Industry Share, the efficient gap varies less over time and the capital wedge is greater. This result suggests that the allocative inefficiency of capital in the manufacturing sector is relatively high. There are two other important points regarding these results. First, the above description refers to the within-industry effect of the misallocation. Therefore, we must to include the between-industry effect of misallocation and compute the total effect to determine the degree of misallocation. Second, the physical capital stock used could affect the capital wedge, particularly in the early years. Accordingly, we use the sub-panel between 2000 and 2011. Furthermore, we obtained the same pattern previously reported.

Figure 2.4 shows the gap between the aggregate manufacturing product and the product implied by the efficient allocation. Basically, this figure represents the results of equations 2.1, 2.8, and 2.9. The line labeled Within-Industry Only shows actual output divided the output

that could be attained if resources were allocated optimally within industry. The line labeled

Between-Industry Onlyshows the output ratio that could be attained if resources were allocated

optimally across all firms in each industry. The line labeledBothshows actual output divided

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by the output that could be attained if resources were allocated across all firms. According to this figure, the gap implied by the within-industry effect varies more than implied by the between-industry effect. Therefore, the misallocation reflects the dynamic effect of the within-industry allocation confirming that the smaller the dispersion of TFP, the lower the misallocation. The lower the misallocation, the smaller the gap is to the effective product. According to this figure, the misallocation falls between 1996 and 2005 and then tends to grow. This pattern is observed in both specifications. In 2005, the lowest year of misallocation, the product is 44.7% farther from the product efficient when using U.S. Industry Share. When we use the Firm-Specific Share, this distance is 54.3%. Thus, an efficient reallocation in times of lower misallocation in the Brazilian manufacturing sector will result in the approximately doubling of the aggregate product. This effect was even greater after 2005.

Using the same metric of Hsieh and Klenow (2009),(𝑌𝐸

𝑡 −𝑌𝑡)/𝑌𝑡, if capital and labor were reallocated optimally within industries, on average, the increase in aggregate value added would be 110.0% (Brazilian Firm-Specific Share) or 161.4% (U.S. Industry Share). In 2005, this effect is smaller and if inputs are optimally reallocate, the increase in aggregate value added would be 73.6% (Brazilian Firm-Specific Share) or 109.0% (U.S. Industry Share). Moreover, these effects would be amplified by between-industry effects and, on average, the optimal reallocation would imply an increase of 128.8% (Brazilian Firm-Specific Share) or 184.7% (U.S. Industry Share). With this additional effect, the reallocation is calculated as 84.0% (Brazilian Firm-Specific Share) and 123.7% (U.S. Industry Share) in 2005. Note that with U.S. Industry Shares, output is away from the efficient optimum. This distance is natural because more of the variation in factor expenditures is attributed to misallocation of resources. However, changes in allocation efficiency are more relevant than the level.

We conducted an additional exercise of reallocation. Following Kambourov (2009) we built a reallocation index that is weighted by the inputs used in each sector relative to the total available in time period𝑡 and𝑡 + 115. Figure 2.5 shows this index calculation for firm-level data from the Brazilian manufacturing sector. From this figure, the between-sector reallocation varies significantly, especially in 2003. However, the within-sector reallocation does not change much over time, except in 2003. Confirming what is shown in figure 2.4, the between-industry effect would amplify the effects of misallocation of resources. This amplification would occur because the reallocation of production factors is performed intertemporally and not always in favor of the firm’s efficiency. Overall, this exercise also implies that misallocation exists. Note that the within-sector allocation index grows between 1996 and 2001 and then tends to fall. This behavior is a relatively similar to that shown in figure 2.4. Thus, changing the form of analysis by examining the dynamic reallocation of factors, we found the same pattern of allocative inefficiency obtained earlier. Therefore, the results suggest that there is misallocation in the Brazilian manufacturing sector, this misallocation is time-variant and the weight of the within-industry effect is substantial.

3.2.2. Measurement error and robustness. We presents some results checks. First, we

acknowledge that in the calculation of these results 1% of the extreme outliers were excluded. However, the results do not significantly change when 5% of these extreme outliers are included. Furthermore, all results were recomputed for a sub-panel from 2000-2011 and another from 1996-2006. Three reasons are considered for this division of the sample. First, this division removes any effect from the construct of the physical capital stock (Oberfield, 2013). Second, the sample was divided because the number of firms in all sectors grew significantly since 2000.

15_{The within-industry allocation index constructs a similar index for reallocation across firms in each industry,} 𝐼W s(𝑡). Then 𝐼W(𝑡)is a weighted average of each industry’s reallocation index, where an industry’s weight is

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Third, the sample was divided to check how the results are sensitive to the reclassification of sectors by the ISIC Rev 3.116_{. However, the previous results do not change substantially for}

these subpanels.

We also check if the metric of misallocation is not really part of the technology level. Figure 2.6 shows the decomposition changes of the Solow residual. In each year three bars are plotted: the log deviation of within-industry allocational efficiency, 𝑑log𝑀 𝑊𝑡; the log deviation of between-industry allocational efficiency, 𝑑log𝑀 𝐵𝑡; and the appropriate Solow residual, 𝑑log𝑌𝑡−𝛼𝑀𝑑log𝐾𝑡−(1−𝛼𝑀)𝑑log𝐿𝑡. If the first two bars add up to the third, then the change in measured aggregate productivity is completely explained by the changes in the extent of misallocation (Oberfield, 2013). However, this result does not occur.

As in other studies (Restuccia and Rogerson, 2008; Hsieh and Klenow, 2009; Buera and Shin, 2013) we consider that𝜎 is equal to 3. Then, we recalculate this result for𝜎equal to 5, similarly other studies. Table 2.3 shows the degree of misallocation of resources for different specifications and values of𝜎. The first and third columns represent the results of figure 2.4. Note that the trend of the results does not change, but the magnitude of the results changes. When𝜎 is equal to 5 the extension misallocation tends to be even higher. This increase in the results was expected because growth in substitutability of the sectors implies that the effect of relative prices are potentiated. Furthermore, it was expected that the between-industry effect did not change because the increase in the degree of substitution between sectors should not have an effect within sectors. Similarly, the distortions include these prices (Restuccia and Rogerson, 2008). Therefore, the extension misallocation grows with the degree of substitution between sectors. However, the dynamics should be identical. This pattern holds in the results and any inferences regarding still valid.

Note that we introduce other specification for the intensity of factors in the last two columns of table 2.3. It is possible that industries in Brazil are qualitatively different from the corresponding industries in the U.S. In that case, the cost shares of U.S. industries provide a poor benchmark for the production parameters of Brazilian firms. Therefore, assume that each Brazilian manufacturing sector is, on average, undistorted. For each industry, we compute the log of the ratio of expenditure on capital to the expenditure on labor in each year, and back out the factor intensities assuming that the median best reflects the true production parameters (Brazil Industry Share). Observe that the trend of resource misallocation is not affected by this specification. However, the degree of misallocation grows considerably. Assuming that the Brazilian manufacturing sector is undistorted is clearly fragile. Thus, this specification will corroborate only the existence of resource misallocation and not the extent of the misallocation. 3.2.3. Economic crisis. The second research question assesses the effect of economic crisis

and the policies that follow. We examine three crises. The Asian financial crisis reduced the availability of capital in the Brazilian economy, which had a recent stabilization of inflation and a regime of fixed exchange rates17_{. The second crisis was a domestic crisis in 2002 caused by}

uncertainties in the Brazilian political situation. Finally, we examine the Subprimes crisis. In figure 2.1 we saw that TFP fell in the Asian financial crisis and too in the Subprime crisis. In 2002, the aggregate TFP seems to have not been affected. If we look at figures 2.3 and 2.4, apparently the misallocation of resources was amplified in 2008. However, the effect of the Asian financial crisis is inconclusive regarding the misallocation of resources in the Brazilian manufacturing sector. The domestic crisis also had an inconclusive effect concerning misallocation of resources. Again, this could occur because more of the variation in factor

16_{The build of the firm-level data uses two modes for classification of economic activities. However, these}

classification methods imply that there is no perfect match between classifications and observations could be lost. Moreover, when firm-level data could be reclassified by ISIC Rev 3.1 a distribution may have changed and, consequently, the weight of each sector in the economy may also have changed.

17_{In fact this crisis occurred between 1997 and 1998. Thus the effects in 1997 could also correlate with this crisis.}

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expenditures is attributed to resource misallocation. This change in specification possibly has detect any the relative effects between the Brazilian and U.S. economies18_{. In resume, these}

results suggest that firms in the Brazilian manufacturing sector react differently to each of crisis. However, in figure 2.2 we saw that there was an increase in the small firms in the Brazilian manufacturing sector. Thus, as verification, we check how the scala wedge varies between firms. Figure 2.7 shows this variation. Here, firms are sorted in 10 groups by the value added. A pattern is clear that the scala wedge of the high-product firms is almost time-invariant. However, this variability is a significant change in the low-product firms. The volatility is higher in those firms and the degree of misallocation of resources grows after a crisis. This effect suggests that low-product firms were relatively more affected by the crisis. Several factors can answer this increased inefficiency, such as the reduced availability of resources in a crisis and the contractual costs of the labor market, especially for low-product firms.

Figure 2.8 shows TFP and misallocation within-industry in each sector for each economic crisis. Here we divide the sectors in durable or non-intensive goods and international trade. We arbitrarily define the trade intensive by sectors that exports or import 30% of total revenue. This figure suggests that the growth of allocation efficiency is positively correlated with TFP growth in the crisis. This outcome was expected. Between sectors there is a significant distinct time period of the crisis. However, we can not affirm that the durable goods or trade-intensity sectors were most affected. Interestingly, these results regarding durable goods differs from the result obtained by Oberfield (2013) for Chile in the crisis of 1982.

Thus, the previous results suggest that misallocation of resources in the Brazilian manufacturing sector was strongly affected by the Subprimes crisis. Small firms were the most affected. The availability of capital, the imperfections in labor market, and the financing constraints in the manufacturing sector, for example, are factors that could explain this increased sensitivity in times of crisis.

4. Extended analysis: linkages, complementarity and tax effects

4.1. Linkages and complementarity. The role of interdependence between sectors is another consideration. We argue that resources are misallocated between firms because, on average, the product is less than the product would be with the optimal use of inputs. However, we do not consider the multiplier effects among sectors (Jones, 2011). Furthermore, this misallocation is implicitly connected to the restriction of resources. Of course, if resources were abundant then there would be no allocation problem. Thus, we also must compute the restriction of inputs. From this, we investigate how the results would change if we extend the basic framework and introduce these elements.

Suppose that the production function of each firm is

(2.12) 𝑋𝑖𝑠𝑡=𝑀𝑖𝑠𝑡(︀

𝐾𝛼𝑖

𝑖𝑠𝑡𝐿

1−𝛼𝑖

𝑖𝑠𝑡 )︀1−𝛾

(︃ ∏︁

𝑠∈𝑆 𝑋𝜅𝑠

𝑠𝑡 )︃𝛾

,

where𝛾 ∈ [0,1) represents the effect of a sector’s output in the production of each firm and

𝜅𝑠 ∈ [0,∞) measures the effect of output by each sector. If 𝛾 = 0 we return to the basic theoretical framework without linkages. If 𝛾 ̸= 0 and 𝜅𝑠 = 0, ∀𝑠 ∈ 𝑆, then 𝛾 represent a measure of underutilization of resources. Finally, if𝛾 ̸= 0and𝜅𝑠 = 1for only the𝑠sector firm itself and zero for all others, then we have a characterization similar to linkages by Jones (2011). Then, the results in the previous section do not computes these sectoral linkages. This effect would be partially included in TFP. Thus𝛾 represents a measure of linkages whereas𝜅would be a measure of complementarity between sectors. The higher the linkages are between sectors, the greater the effect on the production of each firm and thus, for each sector. Intuitively, the

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larger 𝛾, the higher the dependence of firms on the production sectors. Moreover, the higher 𝜅, the higher the effect on each sector. For example, if firms of manufacture of machinery and equipment inefficiently produce less, the availability of goods produced by these firms would affect the production of food products. However, the opposite impact is not necessarily true. Hereafter there would be linkage effects that depend on the sectors’ characteristics.

Assume that there is not firm can alter significantly the production of each sector. Thus, the sectoral output is exogenous to each firm. Then, for equations 2.2 and 2.12 we can find that the production of each sector is

(2.13) 𝑋𝑠𝑡 = ⎡

⎣ ∏︁

𝑠′_∈_𝑆_∖{_𝑠_}

𝑋

𝜅𝑠′(1−𝛾) 1−𝜅𝑠(1−𝛾) 𝑠𝑡

⎤

⎦ [︃

∑︁

𝑖∈𝐼𝑠

(︀

𝑀𝑖𝑠𝑡(𝐾𝑖𝑠𝑡𝛼𝑖𝐿1𝑖𝑠𝑡−𝛼𝑖)𝛾 )︀𝜎−_𝜎1

]︃₍_𝜎 𝜎

−1)(1−𝜅𝑠(1−𝛾)) .

The equation above confirms that the production of each sector𝑠grows with the production of other sectors𝑠′ _∈ _𝑆_{∖ {𝑠}. Furthermore, the greater}_𝜅

𝑠, the higher the complementarity effect. The greater the linkages in the economy and the more connected the sectors, the greater the production is in each sector and the greater the production of the final good. From this, we could have a situation where there is a high misallocation in some sectors, but the inputs are allocated in an aggregately efficient manner towards these sectors. This hypothetical sectors could have a connection elevated to other sectors in the economy and it would generate a higher aggregate product.

Similar to equations 2.5a and 2.5b we have 𝑀 𝑅𝑃 𝐿𝑖𝑠𝑡 =

[︂

1 1−𝛾+𝛾∑︀

𝑠∈𝑆𝜅𝑠𝜂𝐾𝑖𝑠𝑡/(1−𝛼𝑖)

]︂ [︂

1 1−𝜏𝑌 𝑖𝑠

]︂ 𝑤𝑖𝑠𝑡, (2.14a)

𝑀 𝑅𝑃 𝐾𝑖𝑠𝑡=

[︂

1 1−𝛾+𝛾∑︀

𝑠∈𝑆𝜅𝑠𝜂𝐿𝑖𝑠𝑡/𝛼𝑖

]︂ [︂

1 +𝜏𝐾𝑖𝑠

1−𝜏𝑌 𝑖𝑠 ]︂

𝑅𝑡, (2.14b)

where 𝜂𝑧𝑖𝑠𝑡 = (𝑧𝑖𝑠𝑡/𝑋𝑠𝑡) (𝜕𝑋𝑠𝑡/𝜕𝑧𝑖𝑠𝑡) such that 𝑧𝑖𝑠𝑡 = {𝐾𝑖𝑠𝑡, 𝐿𝑖𝑠𝑡}. Therefore, 𝜂 measures

how sectors are affected by the resource choice at firm-level. Assume that the inputs are finite in each time period. Then, implicit in 𝜂 would be some input restriction that also affect the optimal allocation at the firm-level in each sector. Observe that this effect would depend on the available amount of capital and labor. Furthermore, note that𝜅is sector-variant, but𝜂and𝛼are firm-variant. Then, from equations 2.14a and 2.14b the effects of linkages, the complementarity, and the input constraint would be summarized for parameters𝛾,𝜅, and𝜂, respectively.

Observe that in equations 2.14a and 2.14b the product 𝜅𝜂/𝛼 intuitively represents an interdependence between sectors in terms of resource utilization. This term attenuate the distortion effect of resource allocation presented in the basic framework. If each firm is not large enough in relation to the economy, then𝜂tends to be very low and it effect is amplified by the capital share. For example, suppose that𝛾 = 0.1and all firms manufacturing food products and beverages haves𝛼 = 0.3and some connection with 10 other sectors. In addition, assume that𝜂 = 0.01and𝜅 = 0.5. In this conjecture, for equation 2.14b, this extension implies that approximately 10% of the misallocation of inputs at the firm-level detected is actually the effect of linkages and complementarity. Furthermore this effect increase with 𝛾 and decrease with 𝜂. However, the higher the linkages between sectors are, the lower this the effect. If we have 20 sectors for these same parameters, the result above drops to approximately 8%. Intuitively, the larger the quantity of sectors in the economy with linkages is, the stricter the allocation of inputs (intermediate good, capital, and labor) and the smaller the misallocation of resources. This follows the central idea of Jones (2011).

This brief extension can partly explain the elevate (and persistent) degree of misallocation that we found in key-sectors of Brazilian manufacturing, for example, in the manufacture of machinery and equipment. These key-sectors has high linkages. Thus, the misallocation of

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resources would not be undesirable in terms of aggregate performance in that misallocation implies an allocative bias towards these sectors. However the most prominent problem is the necessity to improve the production efficiency of these the key-sectors19_.

We no have information in the firm-level data regarding intermediate consumption in Brazilian firms. This lack of information makes it impossible to clearly identify the effects of linkages. Furthermore, we perform an illustrative exercise regarding this characterization. Table 2.4 shows how linkages and complementarity will affect marginal revenue of product. This is the effect of the first term in equations 2.14a and 2.14b20_{. We expect the higher}

𝛾 the higher variation of𝑀 𝑅𝑃 𝐾. However the this effect is minor to greater is𝜂. Therefore, for the same level of linkages, the higher𝜂is the lower the effect of𝑀 𝑅𝑃 𝐾. We expect this the same pattern in𝑀 𝑅𝑃 𝐿. But we also expect the higher effects of linkage and complementarity is computed in𝑀 𝑅𝑃 𝐿. This fact is direct result of fact that the labor share is higher to the capital share. The results in table 2.4 corroborate this expectation. Finally and fundamentally this exercise suggests that the higher the linkages and the stricter the availability of resources implies a greater effect on the computed misallocation of resource at the firm-level that would not result in productive inefficiency.

4.2. Tax. Another factor that distorts the allocation of resources is the tax system because taxation affects the relative price of goods. Taxes also indirectly affect the efficiency of production between sectors because they can finance a productive public good, for example. Thus, taxation is substantially related to misallocation of resources. If we measure misallocation without the effect of tax, then we would have a measurement of how the Brazilian tax system is prejudicial to manufacturing. Table 2.2 shows the ratio of the tax the value added for each sector in Brazil. There is some variability between sector. This also occurs between years in some sectors. Therefore, the tax system will also differently affect each sector. These asymmetric effects can affect the misallocation of resources at the firm-level and, consequently, the performance of aggregate output.

We show how the results are affected in the hypothetical case where there is not taxation. Clearly, the perfect check is not possible. Taxes affect the relative prices and decision-making by agents. With this, the firm’s product, the level of efficiency, and the dynamic effect of the allocation of resources would be affected. Therefore, we present a qualitative exercise. We recalculate the equations 2.6 and 2.7 such that all the taxed value magically becomes product. From this, the degree of misallocation does not change if the tax system does not distort because taxation should not change the dispersion. Figure 2.9 presents what would be the loss of efficiency in aggregate output because of taxation. This figure suggests that the taxation would reduce the misallocation in 0.1-0.5% per year. From the magnitude of this result it is not possible to affirm that tax directly affects misallocation of resources at the firm-level, consequently, the aggregate output.

5. Concluding remarks

This chapter investigates the existence of misallocation of resources in the Brazilian manufacturing sector as well as measuring possible distortions. This chapter also inquires how

19_{We are assuming a closed economy. Furthermore, the linkages and complementarity effects of some specific}

sectors should be relatively higher in others economies. For example, in the INDSTAT database exports are large in the manufacture of motor vehicles, trailers and semi-trailers. The import of inputs in the manufacture of machinery and equipment sectors is elevated. In these cases, the effects of linkages on the sectoral output in the domestic economy may be low because the foreign production increases. However, we get these linkage effects if this process occurs in the foreign economy as opposed to the domestic economy.

20_Each_𝜅_{was imputed using the input-output relationship constructed by Guilhoto and Filho (2010). Thus, we}

Essays on economic growth

ESSAYS ON ECONOMIC GROWTH

ESSAYS ON ECONOMIC GROWTH

ESSAYS ON ECONOMIC GROWTH

ACKNOWLEDGMENTS

ABSTRACT

RESUMO

Contents

List of Figures

List of Tables

Introduction

Misallocation in the Brazilian manufacturing sector